Performance of Full-Duplex One-Way and Two-Way Cooperative Relaying Networks

ABSTRACT

The instantaneous channel SNR is γ = |h| 2 P/σ 2 where, h is channel coefficient, σ 2 is noise power. The normalized transmitted powers of a node S, relay, node D are P S = 1 ,P R = 1 , P D = 1 respectively and the residual self interference channels are assumed to be identical, i.e. γ ̅ SS = γ ̅ RR = γ ̅ DD = γ ̅ LI . For FD-TWR, the relay simultaneously receives signals from both source nodes A and B, and the residual self-interference caused by its co-channel transmission signal and then forwards them to the corresponding destination nodes B and A. The destination nodes B and A simultaneously receive signals forwarded by the relay and residual self-interference created by their co-channel transmitted signals.In the k-th time slot, the signals received at the relay(R), nodes D and S can be expressed as,

y R [k] = h SR x S [k] + h DR x D [k] + h RR t R [k] + n R [k]
(1) where t R [k] , t D [k] and t S [k] are the transmitted signals of the relay, nodes D and S respectively.

PERFORMANCE MODEL
The performance of the DF based Full Duplex and AF based FD relay is presented here.

DF based FD -TWR
The DF based FD-TWR with PNC, the relay decodes the signals received from both source nodes S and D, and then it implements PNC to recode the decoded data and forwards the recoded data to the destination nodes D and S. After receiving the network coded signals from the relay, the nodes D and S perform decoding to obtain their desired data, respectively. For the DF based FD-TWR with PNC, in k-th time slot, the signal transmitted at the relay can be expressed as, Then, the instantaneous SNR of the signal received at the relay can be expressed as, Substitute equation (4) in (2) and (3) Since both destination nodes D and S know their preciously transmitted data, they can subtract the back-propagating self interference in (6) and (7) after decoding, through bit-level XOR operation. The instantaneous SNRs of signals received at nodes D and S can be respectively expressed as, Similarly at node S,
According to [(5), (3)] the outage probability of DF based FD-OWR is, The comparison of (24) and (25) reveals that the outage probability of the DF based FD-TWR with PNC is higher than that in the DF based FD-OWR, because residual self interference, generated at the destination nodes due to their co-channel transmission, deteriorates the SNRs of the received signal.

AF based FD -TWR
In the AF based FD-OWR, in the k-th time slot, the signal transmitted by the relay is the amplification of the prior received signal and it can be expressed as, Where is the amplification factor, which depends on the channel coefficients, and is the processing delay. Sub equation (1) in (26) [ ] = (ℎ The instantaneous transmitted power is expressed as, Considering the power constraint of P R at the relay and assuming that its transmitting power is ε{|t R [k]| 2 } = P R = 1. (30) Since the node D know their transmitted symbols, the back-propagating self-interference can be subtracted.
Similarly at node D, Equation (34) and (35) indicate that FD-TWR has more residual self-interference compared to FD-OWR because all the nodes in FD-TWR operate in full-duplex mode, while only the relay in FD-OWR operates in this mode. Thus, FD-TWR deteriorates the SNR of the received end-to-end signal.
The average rate for the AF based FD-TWR is defined as, In order to obtain a tightly lower bound easily, the constant term −( ̅ + 1) 2 can be discard in the denominator. Then, Here, the residual self interference is assumed to be identical, then ̅ = ̅ = ̅ = ̅ Sub equation (39) The average rate of FD-TWR from source to destination, (42) Then substitute equation (41) and (42) in (36).The average rate for the AF based FD-TWR is, The average rate for the AF based FD-OWR is, The AF based FD-TWR cannot achieve full time multiplexing gain, compared with FD-OWR, because it also suffers from the residual self-interference at the two destination nodes.

Outage probability
Let ℎ = 2 ℎ − 1, where ℎ and ℎ are the outage SNR and rate thresholds, respectively. Thus, the outage probability of FD-TWR is defined as, = {min(log 2 (1 + ), log 2 (1 + )) < ℎ } For the AF based FD-TWR, the integral domain for its outage probability consist of Then, the outage probability of AF based FD-TWR is given in (45).
(45) From the equation (45) 2,1 and 2,2 is represented as, Equation (46) can be written as, The outage probability of the AF based FD-TWR can be tightly upper bounded by, Sub 2,1 and 2,2 in equation (45) Indonesian Where (. ) is the modified Bessel function of the second kind.The outage probability of AF based FD-OWR is, The outage probability of the AF based FD-TWR is higher than that in FD-OWR. This is because the residual self-interference generated at the destination nodes in FD-TWR deteriorates the SNR of the received signals. This also reveal that time multiplexing can help to improve the average rate, but simultaneously it also leads to a loss in the outage performance.

SIMULATION RESULTS
In this section, the performance of the FD-TWR scheme is presented using MATLAB simulations. The average rate and Outage probability of FD-TWR scheme are presented.
In Figure 2 the outage probability of the DF based FD-TWR and FD-OWR with PNC under the outage rate threshold, ℎ = 1 b/s/Hz is shown. In this FD-TWR achieves better performance than the FD-OWR, because the DF based FD-TWR suffers from more severe residual self-interference than FD-OWR. It is also shown that PNC can improve the outage performance of the DF based FD-TWR, because it enables the relay to forward the signals with maximum power without performing power allocation, which improves the quality of the relaying link. In this the loop interference can be varied with respect to 3 dB, 6 dB, and 10 dB.  Figure. 4 compares the average rate of the DF based FD-TWR and FD-OWR with physical layer network coding. The results show that the DF based FD-TWR can achieve higher rate than FD-OWR. Besides, PNC can improve the rate for the DF based FD-TWR in the low SNR region. In this the loop interference can be varied with respect to LI=3 dB and LI=10 dB. At 10 dB FD-TWR transmits 2.3 b/s and FD-OWR transmits 1.6 b/s. Then at 3 dB FD-TWR transmits 3.8 b/s and FD-OWR transmits 3 b/s. The average rate of the AF based FD-TWR and FD-OWR with physical layer network coding is compared in Figure 5. The DF based FD-TWR can achieve higher rate than FD-OWR. The loop interference is varied with respect to LI=3 dB and LI=10 dB and the performance is evaluated. At 10 dB FD-TWR transmits 1.6 b/s and FD-OWR transmit 0.7 b/s. Then at 3 dB FD-TWR transmits 2.4 b/s and FD-OWR transmits 1.6 b/s.

CONCLUSION
The outage probability and average rate of FD-TWR and FD-OWR using a physical layer network coding was analytically derived. The performance evaluation was done for relaying protocols like DF and AF schemes employing Physical network coding. The outage probability of the DF based FD-TWR and FD-OWR with PNC under the outage rate threshold, R th = 1 b/s/Hz. In this FD-TWR achieves better performance than the FD-OWR, because the DF based FD-TWR suffers from more severe residual selfinterference than FD-OWR. It is also shown that PNC can improve the outage performance of the DF based FD-TWR, because it enables the relay to forward the signals with maximum power without performing power allocation, which improves the quality of the relaying link. The outage probability of the AF based FD-TWR and FD-OWR shows the FD-TWR achieves better performance than the FD-OWR with PNC under the outage rate threshold. The results show that the outage probability of the AF based FD-TWR is higher than that in FD-OWR. The AF based FD-TWR suffers from the residual self-interference not only at the relay but also at the destination nodes, which deteriorates the SNR of the end-to-end link. The average rate of the AF based FD-TWR and FD-OWR with physical layer network coding shows that the DF based FD-TWR can achieve higher rate than FD-OWR.